Simplify the following expression: $ k = \dfrac{q + 9}{-8q} - \dfrac{-5}{7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{q + 9}{-8q} \times \dfrac{7}{7} = \dfrac{7q + 63}{-56q} $ Multiply the second expression by $\dfrac{-8q}{-8q}$ $ \dfrac{-5}{7} \times \dfrac{-8q}{-8q} = \dfrac{40q}{-56q} $ Therefore $ k = \dfrac{7q + 63}{-56q} - \dfrac{40q}{-56q} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{7q + 63 - 40q }{-56q} $ Distribute the negative sign: $k = \dfrac{7q + 63 - 40q}{-56q}$ $k = \dfrac{-33q + 63}{-56q}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{33q - 63}{56q}$